Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ilikephysics2

  • 3 years ago

Find the first 4 terms of the taylor series of sin x at x = pi/4.

  • This Question is Closed
  1. ilikephysics2
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The first 4 derivatives are cos(x) then -sin(x) then -cos(x) and then sin(x)

  2. Algebraic!
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sin(pi/4) + cos(pi/4) * (x-pi/4) -sin(pi/4) * (1/2!) (x-pi/4)^2 .....

  3. ilikephysics2
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is that it?

  4. Algebraic!
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    pretty straightforward.. what was your question about?

  5. Algebraic!
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that's the first 3 terms... you should be able to get the 4th now?

  6. ilikephysics2
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That does not look right though

  7. Algebraic!
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well... I lied a bit... a few of those terms are zero...

  8. Algebraic!
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but you can work from them... right?

  9. RadEn
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    f(x) = f(x0) + (x-x0)*f'(x0)/1! + (x-x0)^2*f"(x0)/2! + (x-x0)^3*f'"(x0)/3!

  10. RadEn
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    with x0 = pi/4, for f(x) = sinx --> f(pi/4) = sin(pi/4) = 1/2*sqrt(2) f'(x) = cosx --> f'(pi/4) = cos(pi/4) = 1/2*sqrt(2) f"(x) = -sinx --> f"(pi/4) = -sin(pi/4) = -1/2*sqrt(2) f'"(x) = -cosx --> f'"(pi/4) = -cos(pi/4) = -1/2*sqrt(2) now, just subtitute all numbers above to generally formula !!!

  11. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy